Cleverley was the subject of a tackle by Kevin Davies in the 5-0 win over Bolton on Saturday.
United expect the England Under-21 midfielder to be out for four weeks which is an improvement on the forecast yesterday when they feared a fracture would have meant he was unable to play for months.
The 22-year-old will miss England's Euro 2012 qualifier against Montenegro next month but should be available for November's matches, when national team manager Capello has pencilled him in to make his debut.
Providing England have collected the point against Montenegro they need to book a place at Euro 2012, Capello has said he plans to blood Cleverley and Phil Jones in a November friendly which is expected to be against Spain.
"They will play in the next friendly games," said Capello.
"They will play, possibly in a really short time.
"I remember (Jack) Wilshere. When he started the season he was not OK. In November he was.
"Good players don't have an age. The quality of these players is more important.
"If we qualify, it will be an important chance for these players to play."
Manchester United manager Sir Alex Ferguson, who condemned Davies' tackle, will have been cheered by the news one of his rising stars is out for weeks rather than months.
But he confirmed Jonny Evans and Patrice Evans are doubtful for Wednesday's Champions League clash with Benfica in Lisbon.
"Jonny is doubtful for Wednesday," Ferguson told MUTV.
"He got a knee in the hip in the second half which was pretty painful, while Patrice got a kick on the kneecap."